The invention relates to the determination of the particle size distribution and zeta potential of particles in a colloidal system.
This invention deals with a particular kind of dispersed system (or colloid), which can be described as a collection of small particles immersed in a liquid. These particles can be either solid (suspensions) or liquid (emulsions). Such dispersed systems play an important role in paints, lattices, food products, cements, abrasives, minerals, ceramics, blood, and enumerable other applications.
These systems have a common feature. Because of the small particle size, the total surface area of the particles is large relative to their total volume. Therefore surface related phenomena determine their behavior in many processes. This invention has particular application to dispersed systems where these surface effects are dominant, corresponding to a range of particle size up to about 10 microns. The importance of these surface effects disappears for larger particles.
In particular, this invention deals with concentrated dispersed systems, which are different from dilute systems because of the importance of particle-particle interactions. The boundary between dilute and concentrated systems is somewhat subjective and may vary from 1% vol to 10% vol depending on the measuring technique. We will use the boundary of 2%-5% vol suggested by Hunter in his recent review of electroacoustics. (Hunter, R. J. xe2x80x9cReview. Recent developments in the electroacoustic characterization of colloidal suspensions and emulsionsxe2x80x9d, Colloids and Surfaces, 141, 37-65, 1998)
The characterization of such concentrated suspensions and emulsions is important not only for the manufacture, but also the development of new systems with improved properties. There are two basic notions for characterizing these dispersed systems: xe2x80x9cparticle size distributionxe2x80x9d and xe2x80x9czeta potentialxe2x80x9d. Several methods are known for determining these characteristics. Most methods are based on light, for example: microelectrophoresis; light scattering; light diffraction; etc. There is a new alternative method based on ultrasound that is rapidly becoming important. This ultrasound method has a big advantage over traditional light-based techniques because it is able to characterize a concentrated system without dilution. Light-based methods usually require extreme dilution in order to make the sample sufficiently transparent for measurement. This invention deals with improvements of this ultrasound characterization technique.
There are two methods for ultrasound characterization of disperse systems: Acoustics and Electroacoustics. This invention deals only with Electroacoustics. An electroacoustic method applies an acoustic input and measures an electrical response, or conversely applies an electrical input and measures an acoustic response.
This electroacoustic method involves two steps. The first step is to perform an experiment on the disperse system to obtain a set of measured values for certain macroscopic properties such as temperature, pH, Colloid Vibration Current, etc. The second step is an analysis of the measured data to compute the desired microscopic properties such as particle size or xcex6 (zeta) potential. Such an analysis requires three tools: a model dispersion, a prediction theory, and an analysis engine.
A xe2x80x9cmodel dispersionxe2x80x9d is an attempt to describe the real dispersion in terms of a set of model parameters including, of course, the desired microscopic characteristics. The model, in effect, makes a set of assumptions about the real world in order to simplify the complexity of the dispersion and thereby also simplify the task of developing a suitable prediction theory. For example, most particle size measuring instruments make the assumption that the particles are spherical and therefore a complete geometrical description of the particle is given by a single parameter, its diameter. Obviously such a model would not adequately describe a dispersion of carpet fibers that have a high aspect ratio and any theory based on this over-simplified model might well give incorrect results. The model dispersion may also attempt to limit the complexity of the particle size distribution by assuming that it can be described by certain conventional distribution functions, such as for example a lognormal distribution.
A xe2x80x9cprediction theoryxe2x80x9d consists of a set of equations that describes some of the measured macroscopic properties in terms of these microscopic properties of the model dispersion. For example, a prediction theory for Electroacoustics would attempt to describe a macroscopic property such as the colloid vibration current in terms of such microscopic properties as the particle size distribution and zeta potential.
An xe2x80x9canalysis enginexe2x80x9d is essentially a set of algorithms, implemented in a computer program, which calculates the desired microscopic properties from the measured macroscopic data using the knowledge contained in the prediction theory. The analysis can be thought of as the opposite or inverse of prediction. Prediction describes some of the measured macroscopic properties in terms of the model dispersion. Analysis, given only the values for some of the model parameters, attempts to calculate the remaining properties by an analysis of the measured data. There are many well-documented approaches to this analysis task.
There are two different approaches to electroacoustic measurements. The first approach employs an electric field to cause the particles to move relative to the liquid. This particle motion generates an ultrasound signal that can be measured. This is the so-called Electrokinetic Sonic Amplitude (ESA) approach. It is described by Oja (U.S. Pat. No. 4,497,208), O""Brien (U.S. Pat. No. 5,059,909), and Cannon (U.S. Pat. No. 5,245,290).
The second approach is the reverse of the first: an ultrasound wave makes the particles move and a resultant electric signal is measured. The electrical signal can be expressed as either a Colloid Vibration Potential (CVP) or a Colloid Vibration Current (CVI), depending on whether one measures the open circuit voltage or the short circuit current between two suitable electrodes. The CVI mode is preferable because it eliminates the need to measure the complex conductivity, which would otherwise be required to calculate the desired xcex6 potential. Marlow (U.S. Pat. No. 4,907,453) and Cannon (U.S. Pat. No. 5,245,290) describe this CVI approach.
In principle, the Electroacoustic signal contains information about both particle size and zeta potential. O""Brien suggests using such electroacoustic measurements at multiple frequencies for characterizing both parameters, the so-called xe2x80x9cO""Brien method (Column 4). Cannon describes an implementation of this process into a particular device.
There are two main aspects of O""Brien""s claims (Column 4, lines 15-22),
xe2x80x9c(1) A method for determining particle size and charge from measurement of particle velocity in an alternating electric fieldxe2x80x9d
xe2x80x9c(2) A method of obtaining that particle velocity from measurements of the interaction of sound waves and electric fields in the suspension.xe2x80x9d
From this it becomes clear that the notion of the xe2x80x9cparticle velocityxe2x80x9d or xe2x80x9cparticle dynamic electrophoretic mobilityxe2x80x9d (O""Brien, Column 4, lines 30-65) is an essential part of the invention. O""Brien""s method [Column 10, line 15, Equation 7] relies heavily on the notion of a xe2x80x9cdynamic electrophoretic mobilityxe2x80x9d xcexc and proposes a very simply relationship between xcexc and the measured electric current produced by the sound wave xcex1 given by:                     α        =                                            ϕ              ⁢                              xe2x80x83                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              ρ                        ρ                    ⁢          μ                                    (        1        )            
where xcfx86 is the volume fraction of the particles, xcfx81 is a solvent density, and xcex94xcfx81 is the difference between the density of the particles and the density of the solvent.
Equation (1) follows from O""Brien""s reciprocal relationship suggested in O""Brien, R. W. xe2x80x9cElectro-acoustic Effects in a dilute Suspension of Spherical Particlesxe2x80x9d, J.Fluid Mech., 190, 71-86 (1988)
In point of fact, both theoretical considerations and experimental evidence prove conclusively that Equation 1 is not valid for concentrated systems. From a theoretical viewpoint the equation contradicts the general Onsager principle. Furthermore, the use of O""Brien""s equation results in zeta potential errors as large as an order of magnitude when experiments are made with typical concentrated silica or rutile slurries.
Equation 1 purportedly relates an experimentally measured parameter (xcex1) with a theoretical parameter (xcexc) with a coefficient that is deemed independent of frequency. It is assumed that the frequency dependence can be completely incorporated into the xe2x80x9cdynamic electrophoretic mobilityxe2x80x9d term, which is the main reason for introducing this notion into electroacoustic theory. However, this simple Equation 1 does not work. It is impossible to connect xcex1 and xcexc in a concentrated system using a frequency independent coefficient.
O""Brien""s method attempts to account for particle-particle interaction using a Levine xe2x80x9ccell modelxe2x80x9d (Column 8, lines 50-65). (.Levine, S. and Neale, G. H. xe2x80x9cThe Prediction of Electrokinetic Phenomena within Multiparticle Systems.1.Electrophoresis and Electroosmosis.xe2x80x9d, J. of Colloid and Interface Sci., 47, 520-532 (1974)). However, it is known that the Levine cell model does not provide a correct transition to the Smoluchowski law (Kruyt, H. R. xe2x80x9cColloid Sciencexe2x80x9d, Elsevier: Volume 1, Irreversible systems, 1952), which is known to be valid in concentrated systems.
Historically there have been two different approaches to the development of electroacoustic theory. The first began with works by Enderby and Booth (Booth, F. and Enderby, J. xe2x80x9cOn Electrical Effects due to Sound Waves in Colloidal Suspensionsxe2x80x9d, Proc. of Amer.Phys.Soc., 208A, 32 (1952);Enderby, J. A. xe2x80x9cOn Electrical Effects Due to Sound Waves in Colloidal Suspensionsxe2x80x9d, Proc.Roy.Soc., London, A207, 329-342 (1951)). They simply tried to solve a system of electrokinetic equations without using any reciprocal thermodynamic relationships. It was very complex because they took into account surface conductivity effects, yet it still was valid only for dilute systems. Marlow and Fairhurst (Marlow, B. J., Fairhurst,D. and Pendse,H. P., xe2x80x9cColloid Vibration Potential and the Electrokinetic Characterization of Concentrated Colloidsxe2x80x9d, Langmuir, 4,3, 611-626 (1983)) continued this approach, but tried to extend it to concentrated systems by introducing the Levine cell model. Unfortunately, this approach leads to somewhat complicated mathematical formulas.
O""Brien later suggested a completely different approach by introducing the term dynamic electrophoretic mobility xcexc and deriving the reciprocal relationship expression given in Equation 1, relating this parameter to the measured electroacoustic parameters, such as Colloid Vibration Current (CVI) or Electrokinetic Sonic Amplitude (ESA).
For a time, the introduction of this dynamic electrophoretic mobility appeared to simplify electroacoustic theory by splitting it into two independent problems. The first problem is to develop a theory that relates this dynamic electrophoretic mobility to other properties of the dispersed system. The second problem is to then find a relationship between this dynamic mobility and the measured electroacoustic signal.
However, one important question remained unsolved. In principle, O""Brien""s approach and the Enderby-Booth-Marlow-Fairhurst approach (EBMF) should give the same result, but it is not clear if this is the case. The EBMF theory is somewhat more basic. It needs only major well-tested electrokinetic equations. It also can be checked out for Onsager symmetry relationship.
The applicant describes a new improved theory of electroacoustics that allows one to interpret data over a wide range of concentration up to 50% by volume. We describe a new electroacoustic sensor for making the necessary CVI measurements, electronics for processing this data, additional algorithms for calculating the CVI from the raw data, and means for accurately calibrating the results.
The applicant replaces O""Brien use of dynamic mobility with an improved approach that more accurately relates the parameter a with the properties of the concentrated system. This new theory properly accounts for particle-particle interaction and therefore works even in concentrated systems. Instead of the Levine cell model, the applicant relies on the Shilov-Zharkikh cell model (Shilov, V. N., Zharkih, N. I. and Borkovskaya, Yu. B. xe2x80x9cTheory of Nonequilibrium Electrosurface Phenomena in Concentrated Disperse System 1. Application of Nonequilibrium Thermodynamics to Cell Model.xe2x80x9d, Colloid Journal., 43,3, 434-438 (1981); Dukhin, A. S., Shilov, V. N. and Borkovskaya Yu. xe2x80x9cDynamic Electrophoretic Mobility in Concentrated Dispersed Systems. Cell Model.xe2x80x9d, Langmuir, accepted), which satisfies Smoluchowski law.
In addition to the basic prediction theory, the applicant also changes the perception about the measurement algorithm. O""Brien""s method stresses at several points the necessity of knowing an absolute value of the electroacoustic current (i0) and the absolute value of the pressure difference across the cell (Column 11, lines 25-40). Applicant treats the electroacoustic cell as a transmission line with some energy losses due to the reflection and attenuation. This new approach gives experimental data that is already normalized by pressure. It eliminates the need for absolute values, replacing them with relative numbers using energy conservation law.
The use of a different algorithm for measuring the electroacoustic signal requires very different hardware, as compared to Cannon. The applicant""s electroacoustic sensor contains a piezoelectric transducer with quartz delay as the transmitter and an antenna as the receiver. The transmitter and receiver are either mounted separately in a flow-through design or combined to form a probe design that eliminates effects due to colloid attenuation.